Hi @dacap, thank you for the reply - much appreciated!
Edited my previous reply as I tried the registry edit from the post you linked since writing it.
Running it fixed the issue and I am now able to double click .ase and .aseprite files to open them up in Aseprite! Awesome!
However each file still opens up a new instance of Aseprite, which is what the registry file was supposed to fix (rather than my issue) - so that’s a strange / happy coincidence!
So I went through my entire registry and deleted all keys related to aseprite - there were quite a few for older versions too.
After doing this, rebooting and running the .reg file as per the link you posted, everything is working fine and I can now open files by double clicking them and all files now open in the same running instance of aseprite in a new tab!